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  2. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus. A rhombus is a tangential quadrilateral. [10] That is, it has an inscribed circle that is tangent to all four sides. A rhombus. Each angle marked with a black dot is a right angle.

  3. Icositetragon - Wikipedia

    en.wikipedia.org/wiki/Icositetragon

    In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the regular icositetragon, m=12, and it can be divided into 66: 6 squares and 5 sets of 12 rhombs. This decomposition is based on a Petrie polygon projection of a 12-cube.

  4. Golden rhombus - Wikipedia

    en.wikipedia.org/wiki/Golden_rhombus

    (See the characterizations and the basic properties of the general rhombus for angle properties.) The internal supplementary angles of the golden rhombus are: [3] Acute angle: = ⁡ ; by using the arctangent addition formula (see inverse trigonometric functions):

  5. Golden ratio - Wikipedia

    en.wikipedia.org/wiki/Golden_ratio

    The rhombic Penrose tiling contains two types of rhombus, a thin rhombus with angles of ⁠ ⁠ and ⁠ ⁠, and a thick rhombus with angles of ⁠ ⁠ and ⁠ ⁠. All side lengths are equal, but the ratio of the length of sides to the short diagonal in the thin rhombus equals ⁠ 1 : φ {\displaystyle 1\mathbin {:} \varphi } ⁠ , as does the ...

  6. Rhomboid - Wikipedia

    en.wikipedia.org/wiki/Rhomboid

    Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled.. The terms "rhomboid" and "parallelogram" are often erroneously conflated with each other (i.e, when most people refer to a "parallelogram" they almost always mean a rhomboid, a specific subtype of parallelogram); however, while all rhomboids ...

  7. Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_theorem

    In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

  8. Rhombille tiling - Wikipedia

    en.wikipedia.org/wiki/Rhombille_tiling

    When more than one type of rhombus is allowed, additional tilings are possible, including some that are topologically equivalent to the rhombille tiling but with lower symmetry. Tilings combinatorially equivalent to the rhombille tiling can also be realized by parallelograms, and interpreted as axonometric projections of three dimensional cubic ...

  9. Corresponding sides and corresponding angles - Wikipedia

    en.wikipedia.org/wiki/Corresponding_sides_and...

    The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle a appearing between sides a and b then its corresponding vertex angle v must appear between sides v and w.

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